Displaying similar documents to “Covering properties in countable products, II”

On spaces with point-countable k -systems

Iwao Yoshioka (2004)

Commentationes Mathematicae Universitatis Carolinae

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This paper deals with the behavior of M -spaces, countably bi-quasi- k -spaces and singly bi-quasi- k -spaces with point-countable k -systems. For example, we show that every M -space with a point-countable k -system is locally compact paracompact, and every separable singly bi-quasi- k -space with a point-countable k -system has a countable k -system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable k -systems. ...

Addition theorems and D -spaces

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is proved that if a regular space X is the union of a finite family of metrizable subspaces then X is a D -space in the sense of E. van Douwen. It follows that if a regular space X of countable extent is the union of a finite collection of metrizable subspaces then X is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a D -space. Some other new results on the properties of spaces which are unions of a finite collection of...